Remark 2Let
be an Euclidean domain such for every
we can choose a canonical associate denoted
by normal(
) and called the normal form of
.
Because of the polynomial case, the unit
such
that
normal
is denoted
lc(
) and called the leading coefficient of
.
Then normal(
) where
is the result
of Algorithm 1 can be called
THE GCD of
and
.
This leads to the following AXIOM code.